Numerical analysis

branch of mathematics that studies vector spaces and linear transformations

study of algorithms that use numerical approximation for the problems of mathematical analysis

broad class of computational algorithms using random sampling to obtain numerical results

An approximation is anything that is intentionally similar but not exactly equal to something else.

any digit of a number within the measurement resolution of that number, as opposed to spurious digits

family of algorithms for finding the definite integral of a function

family of implicit and explicit iterative methods

numerical integration

algorithm for polynomial evaluation

theory of getting acceptably close inexact mathematical calculations

technique used in advanced mathematics

also known as absolute error

discrete analog of a derivative

numerical method in which the n-th approximation of the solution is obtained on the basis on the (n-1) previous approximations

type of polynomial used in Numerical Analysis

property of a numerical algorithm which describes how errors and approximations in the input data or intermediate values propagate through the algorithm without diverging its results

approximation of a function by its tangent line at a point

recursive method to evaluate polynomials in Bernstein form, used to work with Bézier curves

'best' approximation of a function by a rational function of given order

functional relationship F between some input x and output y such that y=g(x) and g is Lipschitz in a neighbourhood of every x

function K of the input x of a well-posed problem which describes how much its variation influences the variation of the output g(x)

various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience

In mathematics and computer science, truncation is limiting the number of digits right of the decimal point.

right|thumb|A solution to a discretized partial differential equation, obtained with the finite element method.

algorithms for estimating the derivative of mathematical functions

CORDIC, short for coordinate rotation digital computer, is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots, multiplications, divisions, exponentials, and logarithms with arbitrary base, typically converging with one digit (or bit) per iteration. CORDIC is therefore an example of a digit-by-digit algorithm. The original system is sometimes referred to as '''Volder's algorithm'''.

rate at which a convergent sequence approaches its limit

method for representing and evaluating partial differential equations

boundary set in the complex plane

method for bounding the errors of numerical computations

real-valued function whose value depends only on the distance between the input and some fixed point, which forms a basis for some function space

effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them

element of a basis for a function space

difference between the result produced by an algorithm when using exact arithmetic and when using finite-precision, rounded arithmetic

error from taking a finite sum of an infinite series

class of methods for converting a continuous operator problem to a discrete problem

effective tools for solving ordinary equations, whose working principle is as follows: first we choose a starting point, and then take a small step forward to find the next solution point.

overview about trigonometric tables

presentation of numerical data in a manner that implies better precision than is justified

simultaneous simulation of different aspects of a physical system or systems

mathematical proof at least partially generated by computer

transform in numerical harmonic analysis

interface between statistics and computer science

numerical analysis procedure

harmonic series with all terms containing the digit '9' removed

algorithms in numerical analysis

class of methods used in numerical analysis, scientific computing to solve ODE/PDE

online project meant to be a collection of special functions

algorithm to approximate functions

expression in calculus

mathematical reference work edited by M. Abramowitz and I. Stegun

computation algorithm to sum a sequence of floating-point numbers

study of kind and quantity of error, or uncertainty, that may be present in the solution to a problem

method of evaluating spline curves

expression whose zeros are the integers from 1 to 20

mathematical constant

system of equations that either contains differential equations and algebraic equations

matrix used in finite element analysis

expressions for approximation accuracy

engineering method used when an outcome of interest cannot be easily directly measured, so a model of the outcome is used instead